Video transcript

Let's think about what it
means to multiply 2 over 3, or 2/3, times 4/5. In a previous
video, we've already seen how we can
actually compute this. This is going to be equal
to-- in the numerator, we just multiply the numerators. So it's going to be 2 times 4. And in the denominator, we
just multiply the denominator. So it's going to be 3 times 5. And so the numerator
is going to be 8, and the denominator
is going to be 15. And this is about as
simple as we can make it. 8 and 15 don't have any factors
common to each other, than 1, so this is what it is. It's 8/15. But how, why does that
actually makes sense? And to think about
it, we'll think of two ways of visualizing it. So let's draw 2/3. I'll draw it relatively big. So I'm going to draw 2/3, and
I'm going to take 4/5 of it. So 2/3, and I'm going
to make it pretty big. Just like this. So this is 1/3. And then this would be 2/3. Which I could do a little bit
better job making those equal, or at least closer
to looking equal. So there you go. I have thirds. Let me do it one more time. So here I have drawn thirds. 2/3 represents 2 of them. It represents 2 of them. One way to think about
this is 2/3 times 4/5 is 4/5 of this 2/3. So how do we divide
this 2/3 into fifths? Well, what if we divided each
of these sections into 5. So let's do that. So let's divide each into 5. 1, 2, 3, 4, 5. 1, 2, 3, 4, 5. And I could even divide
this into 5 if I want. 1, 2, 3, 4, 5. And we want to take 4/5
of this section here. So how many fifths
do we have here? We have 1, 2, 3, 4,
5, 6, 7, 8, 9, 10. And we've got to be careful. These really aren't fifths. These are actually
15ths, because the whole is this thing over here. So I should really say
how many 15ths do we have? And that's where we
get this number from. But you see if 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Where did that come from? I had 3, I had thirds. And then I took each
of those thirds, and I split them into fifths. So then I have five
times as many sections. 3 times 5 is 15. But now we want 4/5 of
this right over here. This is 10/15 right over here. Notice it's the
same thing as 2/3. Now if we want to
take 4/5 of that, if you have 10 of something,
that's going to be 8 of them. So we're going to
take 8 of them. So 1, 2, 3, 4, 5, 6, 7, 8. We took 8 of the
15, so that is 8/15. You could have thought about
it the other way around. You could have
started with fifths. So let me draw it that way. So let me draw a whole. So this is a whole. Let me cut it into
five equal pieces, or as close as I can
draw five equal pieces. 1, 2, 3, 4, 5. 4/5, we're going to
shade in 4 of them. 4 of the 5 equal pieces. 3, 4. And now we want to
take 2/3 of that. Well, how can we do that? Well, let's split each
of these 5 into 3 pieces. So now we have
essentially 15ths again. So 1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15. We want to take 2/3
of this yellow area. We're not taking 2/3
of the whole section. We're taking 2/3 of the 4/5. So how many 15ths
do we have here? We have 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12. So if you have 12 of
something, and you want to take 2/3 of that, you're
going to be taking 8 of it. So you're going to be taking
1, 2, 3, 4, 5, 6, 7, 8 or 8 of the fifteenths now. So either way, you get
to the same result. One way, you're thinking
of taking 4/5 of 2/3. Another way you could think of
it as you're taking 2/3 of 4/5.